Phases and Residual Gauge Symmetries of Higgs Models

Abstract

After elimination of the redundant variables, gauge theories may still exhibit symmetries associated with the gauge fields. The role of these residual gauge symmetries is discussed within the Abelian Higgs model and the Georgi-Glashow model. In the different phases of these models, these symmetries are realized differently. The characteristics of emergence and disappearance of the symmetries are studied in detail and the implications for the dynamics in Coulomb, Higgs, and confining phases are discussed.Comment: 30 pages, LaTeX with amsmath macros; updated to include minor corrections in proof; email correspondence to J.W. Negele, negele@mitlns.mit.ed

Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism

“…The operators defined on the left-hand side of Eq. (22) and Eq. (23) expand unambiguously to the vector hybrid tr(F µν 2a A 2aν ) at leading order in the FMS formalism for even N .…”

“…Assuming that the constituent model is valid for this hybrid bound state, the mass will be approximately 2m A2a = 2gv/ √ K. For N odd, we have to use the standard multiplet decomposition to get tr(F µν [A ν , φ 0 ]) = tr(F µν 2a A 2aν ) + tr(F µν f A fν ) in Eq. (22). The mass of the latter can be approximated by 2m A f = gv/ √ K within the simple constituent model.…”

The confinement problem in lattice gauge theory

“…+larger adjoint loops with e −P coefficients (114) The adjoint loops are non-planar contributions, and arise from the "tube" diagrams shown in Fig. 11.…”

Compact Variables and Singular Fields in QCD

“…It is however unlikely that, within the above approximations in treating the restrictions in the range of the gauge field variables, a qualitatively correct description of the magnetic field dominated QCD vacuum [20] can emerge. We note that in the ground state of the Hamiltonian (27), the electric field energy dominates, we have…”

“…These symmetry considerations apply equally well when adjoint matter is coupled to the gauge fields. They have been applied to 1+1 dimensional QCD with adjoint fermions [26] and have shown to be useful in the characterization of the various phases of the Georgi-Glashow model [26,27]. On the other hand, with matter in the fundamental representation present, the system is not anymore invariant under center symmetry transformations, which change the boundary condition of fields carrying fundamental charges.…”